Homework Help:
Probability Question

It is known that the inhabitants of an island tell the truth 1/3 of the time and lie 2/3 of the time. On an occasion, one person made a statement and the person after him said the statement was true. What is the probability that the statement is actually true?

P (1st telling truth | second says first is telling truth) =
P (1st telling truth and second says first is telling truth) / [P(1st is telling truth and second says first is telling truth) + P(1st is lying and second says first is selling truth)]
= 1/3

It is known that the inhabitants of an island tell the truth 1/3 of the time and lie 2/3 of the time. On an occasion, one person made a statement and the person after him said the statement was true. What is the probability that the statement is actually true?

The answer is 1/3. A good way to see this is to do what Claude Bile suggested. Look at the four different "possibilities" one at a time. But you should also ask yourself if they're all really possible. (Big hint: They're not).

I can not say something truthful, and then have my neighbor say something truthful also? theres a 1/3 chance that i would say something truthful, and a 1/3 chance that my neighbor would say something truthful.... no?

The answer is 1/3. A good way to see this is to do what Claude Bile suggested. Look at the four different "possibilities" one at a time. But you should also ask yourself if they're all really possible. (Big hint: They're not).

The answer is not 1/3 .
...
But, since the 2 persons agreed, we know only the first or the last case can be possible.
So, the probability we have a truthful pair of persons is (1/9) / (1/9 + 4/9) = 1/5.

This is classical Bayes.

Yes, you're right. I assigned probability 0 to the impossible "possibilities", but that's not the right way to do this.